To find the coordinates of H' and I' after the translation that maps ∆GHI to ∆G’H’I’, we first need to determine the translation vector based on the coordinates of G and G'.
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Finding the translation vector:
- The coordinates of point G are G(-8, 2) and the coordinates of G' are G'(-1, -3).
- The translation vector can be calculated as follows: \[ \text{translation vector} = G' - G = (-1, -3) - (-8, 2) \] This simplifies to: \[ \text{translation vector} = (-1 + 8, -3 - 2) = (7, -5) \]
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Applying the translation vector to the other vertices:
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We will now apply the translation vector (7, -5) to the other vertices H and I.
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The coordinates of H are H(13, 2). Thus, we apply the translation: \[ H' = H + \text{translation vector} = (13, 2) + (7, -5) \] This gives: \[ H' = (13 + 7, 2 - 5) = (20, -3) \]
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Now, for point I which has coordinates I(-2, 10), we apply the same translation: \[ I' = I + \text{translation vector} = (-2, 10) + (7, -5) \] This results in: \[ I' = (-2 + 7, 10 - 5) = (5, 5) \]
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Final coordinates:
- The coordinates of H' are (20, -3).
- The coordinates of I' are (5, 5).
Therefore, the final coordinates are:
- H': (20, -3)
- I': (5, 5)